The Brahmagupta-Pell equation appears in various contexts in number theory. In this talk, we focus on the polynomial analogue of this equation. This talk will be based on joint works with Akanksha Gupta.

In this talk, I will discuss the extreme (minimum and maximum) values of quadratic twists of modular L-functions associated with a normalized modular form of weight k, evaluated at a horizontal mesoscopic shift from the critical point. I will also discuss some potential arithmetic applications.

Out-of-equilibrium systems are ubiquitous in nature. In contrast to their equilibrium counterparts, which are fairly well-understood using the framework of statistical mechanics, a description of them is challenging and is at the forefront of current-day research. Recently, important experimental and theoretical techniques have been developed, and advances have been made in both classical and quantum systems that are out-of-equilibrium. This conference aims to discuss the current trends in this broad area of research by bringing together experts, early-career researchers, postdocs, and students working in this field. Topics would include (but are not limited to) quantum many-body scars, driven and dissipative systems, disordered, noisy setups, stochastic processes, first-passage problems, and random walks. An important goal is to bring together the community of people working on the classical and quantum fronts and foster collaborations between them. https://www.imsc.res.in/current_trends_classical_and_quantum_out_of_equilibrium_systems_ctcqoes

Out-of-equilibrium systems are ubiquitous in nature. In contrast to their equilibrium counterparts, which are fairly well-understood using the framework of statistical mechanics, a description of them is challenging and is at the forefront of current-day research. Recently, important experimental and theoretical techniques have been developed, and advances have been made in both classical and quantum systems that are out-of-equilibrium. This conference aims to discuss the current trends in this broad area of research by bringing together experts, early-career researchers, postdocs, and students working in this field. Topics would include (but are not limited to) quantum many-body scars, driven and dissipative systems, disordered, noisy setups, stochastic processes, first-passage problems, and random walks. An important goal is to bring together the community of people working on the classical and quantum fronts and foster collaborations between them. https://www.imsc.res.in/current_trends_classical_and_quantum_out_of_equilibrium_systems_ctcqoes

Out-of-equilibrium systems are ubiquitous in nature. In contrast to their equilibrium counterparts, which are fairly well-understood using the framework of statistical mechanics, a description of them is challenging and is at the forefront of current-day research. Recently, important experimental and theoretical techniques have been developed, and advances have been made in both classical and quantum systems that are out-of-equilibrium. This conference aims to discuss the current trends in this broad area of research by bringing together experts, early-career researchers, postdocs, and students working in this field. Topics would include (but are not limited to) quantum many-body scars, driven and dissipative systems, disordered, noisy setups, stochastic processes, first-passage problems, and random walks. An important goal is to bring together the community of people working on the classical and quantum fronts and foster collaborations between them. https://www.imsc.res.in/current_trends_classical_and_quantum_out_of_equilibrium_systems_ctcqoes